### Introduction

The theory of integration forms an important part of mathematical analysis. Historically integration was used to find areas of plane figures. Archimedes used the very same process to find areas of parabola but he called it the*method of exhaustion*. The idea used by Archimedes was to divide the desired area in terms of smaller and smaller areas so that the sum of the areas of these smaller parts tended to a finite limit. It was the genius of Newton (and Leibniz too) to recognize that the process of integration could be viewed as the inverse process of differentiation. This greatly helped in finding areas of curves for which summing the areas of smaller parts was difficult. After Newton people started thinking of integration as the inverse of differentiation and the older approach based on summation was put at the back front.